Near-field acoustic manipulation in a confined evanescent Bessel beam

We demonstrate the potential of using evanescent fields, instead of conventional propagating sound fields, to manipulate particles at micro or nano scale. We generate an evanescent acoustic Bessel beam in liquid above a thin, circular, asymmetrically excited plate. In the sub-MHz ultrasound domain, the resulting radiation force causes the particles to assemble at the pressure antinodes along concentric circles corresponding to the Bessel profile. By imposing an axial confinement in the evanescent region, the subwavelength two-plate sandwich system becomes resonant, increasing the radiation force magnitude. Resonances occur for some well-defined gaps for which whole numbers of antinodal circles are observed. Through fine tuning, particles as small as bacteria can be patterned. Further amplification can be obtained by trapping a microbubble in the Bessel beam axis. As we show, this resonant bubble, which acts as an acoustic magnet, can be used to efficiently capture or repel nearby micro-particles. The development of photonics and plasmonics has seen electromagnetic evanescent waves being used for diverse applications from trapping small particles to illumination in biological applications. As an equivalent to the optics counterpart, the authors report on the generation of an acoustic evanescent Bessel field for acoustofluidic applications that only requires a single piezoelectric element in a sub-wavelength resonant cavity and that can be used to attract or repel particles and cells using acoustic radiation force.

M omentum transfer from radiative electromagnetic and acoustic fields to matter at microscale has been a topic of significant research interest in recent decades. In propagative optics, remarkable applications in trapping microparticles (optical tweezers 1 ) and atoms (laser cooling 2 ) have been achieved. More recently, manipulation by optical evanescent fields, instead of conventional propagating (i.e. radiative) fields, has become possible thanks to the emergence of nano-photonics and plasmonics 3 . Surface plasmons are electromagnetic and evanescent surface modes confined at a metal-dielectric interface. They can give rise to a plasmon radiation force, which has strong potential for optical sorting 4 .
In the meantime, acoustic tweezers have been developed in the radiative acoustic domain, giving birth to a new branch of physics binding acoustics and microfluidics in the field of acoustofluidics 5 . Acoustofluidic chips mainly employ propagative (i.e. radiative) fields mostly based on the use of standing bulk and surface acoustic waves (BAW and SAW, respectively). BAW and SAW (commonly of leaky Rayleigh type) are emitted at high frequency (in the MHz range) to maximize the associated radiation force. Surprisingly, and unlike their electromagnetic counterpart, the use of non-radiative acoustic-based forces has attracted little attention to date. To the best of our knowledge, no prediction of the radiation force in an evanescent acoustic field exists. Likewise, only a few experimental works 6-8 report on manipulation by evanescent acoustic fields. This lack seems paradoxical in view of the main features of evanescent waves. Indeed, regardless of their nature, in a non-radiative field, waves can be confined to an ultra-small region of sub-wavelength dimensions and break the diffraction limit. Besides, their intrinsic in-plane near-field confinement is a key feature of contactless labon-a-chip applications. Furthermore, Durnin 9 was the first to propose Bessel beams in optics as a diffraction-free beam solution of the Helmholtz equation. Bessel beams propagate in free space without undergoing diffraction and retain their transverse pattern as a result. Since then, the optical Bessel field has been the subject of intensive research leading to today's evanescent versions of the Bessel beam (see 10 and references therein). In acoustics, the potency of propagative Bessel beams has recently been demonstrated in the creation of acoustic tweezers using arrays of ultrasonic transducers [11][12][13] , but no evanescent version has been reported so far.
Here, we report on a simple strategy to create an acoustic evanescent Bessel beam for acoustofluidic applications, that only requires a single piezoelectric element. Our present approach stems from 8 , where evanescent waves are favored through the excitation of an ultra-thin circular substrate. At a low frequency, the flexural plate waves are subsonic interfacial guided waves similar to plasmon waves in the electromagnetic domain. In this way, we generate an evanescent Bessel beam of order zero in the liquid above the plate. The beam is firstly analyzed in infinite liquid conditions prior to studying the effect of confinement. As we show, when the Bessel beam is confined to evanescence length, resonances occur in the system and its trapping capabilities are enhanced. Lastly, we demonstrate how this beam can excite a trapped single sub-wavelength resonant bubble thanks to the lowfrequency regime. The microbubble enhancement then competes with the near-field radiation force due to the Bessel beam, enabling either to attract or repel the neighboring particles.

Results
Evanescent acoustic Bessel beam emission. All the devices used in the present study are made of a circular thin glass plate fixed by a double sided tape onto an annular piezoceramic. The ceramic is a ring of 8.5 mm internal radius covered by a 150-μm-thick glass plate. In the first part of this study, a polypropylene cylinder (15 mm inner radius) is used to contain the liquid above the plate. The cylinder is simply taped onto the piezoceramic and filled up with water up to h l = 20 mm (see Fig. 1a). The ceramic is excited at resonance (f = 45 kHz) by a signal generator and an amplifier. The resonant frequency is determined by the electromechanical analysis (electric impedance measurement) of the whole system (see Supplementary Fig. 1 and Methods).
The acoustic pressure amplitude P(r,z) is measured with a needle hydrophone (see Methods) mounted on a 3-axes translation stages setup. The radial dependence for several heights, from 100 μm to 2 mm, is presented in Fig. 1b  The tape internal radius is a = 9 mm. b Normalized acoustic pressure as a function of the radial distance for z ϵ {0.1; 1.1; 2.1} mm in blue, green and pink, respectively. Voltage U = 20 V pp , f = 45 kHz. P is normalized by P 0 = P(r = 0, z = 0.1 mm) = 34 kPa. Solid red line: calculated pressure P assuming a free boundary plate (using Rayleigh integral). Dotted red line: comparison with the full Bessel shape J 0 λ 04 r a À Á þ C 04 I 0 λ 04 r a À Á , having λ 04 = 12.51 and C 04 = 5.10 −6 . Insert: eigenfrequencies of the system (from Eq. 3). Blue: unloaded. Red: infinitely loaded. Dashed green lines correspond to the experimental realization. c Evanescent pressure field for U = 20 V pp . Blue: measures. Solid black line: calculated pressure for a plate amplitude of 0.1 μm. This amplitude is chosen for its best fit with the measured pressure at 1 mm. The higher measured pressures for heights smaller than the sensor radius (750 μm) are assumed to be affected by near field effects between the plate and the sensor membrane. Dashed red: theoretical pressure approached neglecting boundary effects, with P ¼ Pðr ¼ 0; z ¼ 0Þe Àk z z and k z ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi k 2 r À k 2 l q (1/k z = 0.7 mm). Dashed green: linear fit for z ≥ 4 mm. Insert: Pressure amplitude P(r = 0, z = 0.2 mm) as function of the voltage U. Blue: measures. Dashed red: linear fit, with P(kPa) = αU(V pp ) and α ¼ 1 kPa:V À1 pp ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0191-z electroacoustic emission is in the linear regime (see insert Fig. 1c). The radial evolution presents an invariant structure, characteristic of a non diffracting beam, with four pressure nodes of constant position. The whole pattern vanishes exponentially with the distance normal to the plate, as shown on Fig. 1c (on the beam axis). An exponential fit yields to an evanescent decay length of 1/k z = 800 μm, much smaller than the acoustic wavelength in the liquid (λ l = 33 mm).
For a solid plate of thickness h s and density ρ s loaded by a liquid of density ρ l , the plate vertical deflection w obeys a wave equation given by: where D ¼  Table 1) 14 .
The plate vibration is coupled to the normal stress in the liquid by the pressure term at the right hand side: p, which must satisfy the Helmholtz equation Δp þ k 2 l p ¼ 0, where k l = ω/c l and c l the speed of sound in the liquid.
In this system, the effect of loading is classically estimated by assuming that the liquid does not alter the eigenmodes shape but only their frequency 14 . Thus, the nth axisymmetric flexural mode has a deflection W n (r) cos (ωt) following W n ðrÞ=W n ð0Þ ¼ J 0 ðλ 0n r=aÞ þ C 0n I 0 ðλ 0n r=aÞ; ð2Þ where J 0 and I 0 are the ordinary and first order modified Bessel functions of order 0, respectively. The {λ 0n , C 0n } are determined by the boundary conditions at the plate edge 14 . As a result of the liquid load, the eigenfrequencies become smaller as follows where f unload D ρ s h s 1 2 is the n mode unloaded eigenfrequency, with the non dimensional added mass factor Γ 0n that also depends on the plate boundary conditions 14 .
In the absence of loading, the corresponding plate phase velocity is , with ω the driving pulsation. The additional liquid alters the dispersion relation and therefore the corresponding phase velocity c s of plate waves. In both cases, the propagative (radiative) or non-propagative (evanescent) regime of emission is determined by the supersonic or subsonic domain of emission, which is frequency dependent due to the surface waves dispersivity. In particular, for wave modes with c s < c l , no radiation is possible: the regime is subsonic and the normal wavenumber k z is imaginary (evanescent regime). Here the use of very thin substrates in conjunction with low-frequency excitation favors subsonic modes interfacial waves as we will now show.
For any location M in the liquid, the emitted field p ¼ <ðPðMÞe jωt Þ can be calculated by summing up elementary contributions from every point M' of the plate (Rayleigh integral) ∂t 2 e Àjk l r′ dSðM′Þ with r′ = ||MM′|| 15 . This calculation for our thin plate excited at f = 45 kHz assuming free edge conditions yields to the solid lines in Fig. 1b (red) and c (black), in good agreement with experimental data. Note that as in Eq. 2 the I 0 term is negligible away from the borders, the membrane shape can be approached by a Bessel shape, known to be the radial contribution of a cylindrical eigenfunction of the Helmholtz equation 9,16 . As for the normal evanescent profile, the small deviations observed very close to the plate and further than 2 mm are likely to be caused by the sensor perturbation and by the background propagative field emitted by the cylindrical container, respectively. Finally, the insert  Table 2).
Therefore, we conclude that the pressure field in the vicinity of the plate at resonance is well approximated by a n = 4 evanescent Bessel beam where k r = λ 04 /a and k z ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi k 2 r À k 2 l p . As k r ) k l , the loaded plate wave velocity simplifies to Pattern formation. The water is now seeded with polystyrene microparticles (10 and 100 μm) in order to study the behavior of subwavelength particles in the Bessel beam. In the previous setup (infinite liquid condition), no pattern was observed within reasonable times (a few minutes). When the liquid height is reduced down to h l = 1 mm, the acoustic pressure is increased by a factor 2.3 so that a visible pattern starts to form. Note that for small heights (h l ≤ 1 mm), the water can sustain its own weight by capillarity, so that the confining cylinder can be removed, as shown in Fig. 2a. When turning the sound on, particles move toward concentric circles and remain there after the acoustic emission has stopped, as can be seen in Fig. 2b (corresponding Supplementary Movie 1). As also shown, the circles correspond to the pressure antinodes, that stay in the same position as in configuration Fig. 1a since loading negligibly affects the plate modes 14 . This migration is unusual in acoustofluidics regarding the beads acoustic contrast factor which would normally make them move toward the pressure nodes in the Gor'kov framework 17 . Indeed given their density and compressibility ratios,ρ ¼ Besides, we observe that larger particles move noticeably faster than smaller ones. In order to quantify this difference, we restrict ourselves to the first Bessel lobe region (center of the plate) to measure the beads radial velocity. Trajectories are extracted from an automated tracking (TrackMate from ImageJ), as presented in Fig. 2c, from which the particle radial velocities are calculated. Thus, for a 1 mm height drop, we measure a maximal velocity of about 300 μm s −1 for 100 μm beads to be compared with 10 μm s −1 for the 10 μm beads. However, the radial velocity profiles normalized by the maximal value for each particle size are reasonably similar, as shown in Fig. 1d. Interestingly, as also shown in Fig. 2d, with a larger extension displayed on Fig. 2e (blue dots), further decreasing the droplet height to 500 μm yields to a more rapid pattern formation. For this thinner drop, the radial maximal velocity is increased by a factor 6.6, while the pressure raises about a factor 2.4.
Resonance for subwavelength cavity confinment. As suggested by the above mentioned observations, confining the liquid yields to an increased acoustofluidic effect. Hence, having in mind the metamaterial properties of acoustic subwavelength cavities 18 both in terms of sensing 19 or in terms of forces 20 , we now confine the liquid within the evanescence length. For that purpose, a hard cover (1-mm-thick glass plate) is placed at a distance h l in the range 60-890 μm away from the emitter surface. Parallelism is ensured by dedicated machined annular polymethylmethacrylate (PMMA) wedges (see Fig. 3a). In the presence of the cover lid, 10 μm PS beads still gather along the same concentric ring structure. However, when reducing h l , the number of visible rings on the plate increases from 3 to 5 (the outer one being hidden by the piezoelectric). For h l > 470 μm (i.e. k z h l > 0.6), the number of rings remains like the non confined case (see Fig. 3b). The increase in the number of rings when confining liquid can be qualitatively understood by the following reasoning. Given its larger thickness (1 mm), the top plate can be considered as a rigid boundary condition (D / h 3 s , see Eq. 1), so that the fluid normal velocity vanishes at this surface. Its effect can be estimated by considering an equivalent system, with a doubled liquid height and a top plate identical to the emitting one. This trilayer system with h l,eq = 2h l will present no normal motion in the system symmetry plane. For such a system, the plate dynamic writes 21 Assuming that a resonance occurs when a whole number of wavelength is present on the plate, nλ f ≃ 2a yields to an associated with f conf n ðh h Þ plotted in Fig. 3c. This simple model thus suggests the existence of discrete peaked resonances when the frequency is set to f conf n , or equivalently when the height is set to a resonant one, as shown in Fig. 3c for several cavity heights.
Moreover, beads also move faster toward the pressure antinodes for a height close to h l = 270 μm, about a third of the evanescence length (blue dots in Fig. 3d). In order to verify the existence of an optimal height, two experiments have been conducted. In the first one, we measured the electromechanical impedance of the whole system with reduced heights. In Fig. 3d, the blue dots present the evolution of the resonant frequency (minimal impedance) as a function of the height. Again, an optimal height around h l ≈ 270 μm is observed. In the second experiment, a dedicated pierced upper plate drilled in its center in order to insert the needle hydrophone has been designed to probe the pressure field in the gap when moving the cover plate (see Supplementary Fig. 3). The insert of Fig. 3d shows that a resonance still occurs since the pressure amplitude presents a peak around h l = 370 μm. The difference between both values probably stems from the use of a drilled PMMA lid instead of a flat hard one as well as from the intrusiveness of the needle in the near-field.
Migration origin. We now address the issue of the origin of the acoustofluidic force acting on the particle in the near-field region. As noticed earlier (Fig. 2d), the normalized radial velocity of various particles follow the same master curve.
Let us firstly discuss the particle movement in the vicinity of the membrane: do the particles bounce off the plate, roll along it as studied in 22 or do they float in the bulk and are pushed by the acoustic radiation force or streaming flow? For a typical vibration amplitude of the plate estimated to be A~P 0 /(ρ l c l ω) = 50 nm (with P 0 = 20 kPa extrapolated from Fig. 1c), the particle inertia ρ p Aω 2 is much larger than its apparent weight (ρ p − ρ l )g (ρ p Aω 2 =ððρ p À ρ l ÞgÞ ¼ 10 4 ) 1, with ρ p the particle density and g the gravity acceleration), so that the apparent gravity cannot keep the particles in contact with the plate for a long time. Once in the bulk, particles will settle by gravity (sedimentation) over a time τ g ¼ 9ηA=½2r 2 p ðρ p À ρ l Þg. Since τ g is much larger that the acoustic period 2π/ω, the particle won't have time to settle down provided that the acoustic amplitude is large enough so that second-order acoustic effects come into play. Consequently they will eventually be either captured and dragged by the acoustic streaming flow, or pushed by the acoustic radiation force.
As for the streaming, the typical streaming velocity scales like (Aω) 2 /c s = 1 μm s [−123 . This streaming velocity becomes comparable with the particle velocity when using tiny particles as small as 500 nm diameter fluorescent tracers (Supplementary Movie 3) for which we measured a maximal velocity of 2 μm s −1 in a 1-mm drop. Nevertheless, both 10 μm and 100 μm particles move much faster (7 μm s −1 and 284 μm s −1 , respectively, see Supplementary  Fig. 4). The observed difference in magnitude discards a streaming-dominated migration and suggests a radiation force mechanism.
For a subwavelength particle of radius r p ≪ λ l (Rayleigh diffusion regime) in an infinite medium, the radiation force is given by the celebrated Gor'kov formula: , V p being the particle volume 17,24 . Here, the acoustic velocity v 1 is first derived from the linearized Euler equation knowing the pressure field p 1 (Eq. 4), leading to v 1 ¼ p 0 ρ l ω k r J 1 ðk r rÞe r þ k z J 0 ðk r rÞe z ð Þ e Àk z z sinðωtÞ. Assuming this force is balanced by a viscous drag F s ∝ 6πη l r p (v p − v 2 ) 25 (v 2 : streaming), the resulting velocity profile v p (r) is presented in Fig. 2e (magenta curve). Here, the Gor'kov approach clearly fails to predict the radiation force. Unfortunately to date, no near-field expression for the radiation force exists. Using a phenomenological approach, we searched for a corrected expression that is proportional to one of the three secondorder acoustofluidic terms À predicts very well the measured evolution, as opposed to the two other terms (see details in Supplementary Fig. 5). A more detailed analysis of the radial scaling of the streaming also allows to conclude that the migration of the 10-μm beads in the 500 μm drop originates from the near-field radiation force, as shown in Supplementary  Figs 6 and 7. The increase of velocity by a factor of 6.6 when h l is decreased from 1 mm to 500 μm is also in accordance with its quadratic dependence on the pressure, which increases by a factor 2.4 (2.4 2 = 6).
In the Supplementary Note 1, we briefly present two keyapplication of the sub-wavelength confined device. In particular, we show that by thinning the glass substrate down to 30 μm, higher resonant frequencies can be achieved in order to increase the radiation force magnitude. Thus, living organisms as small as bacteria can be patterned along concentric circles thanks to the enhanced radiation force arising from the evanescent field. In addition, we also present a more surprising capability of plasma extraction when dealing with whole blood from patients (see also Methods). These stimulating results are let for future dedicated research.
Use of a trapped resonant bubble. Microbubbles are widely used in microfluidics since they act as a local amplifier of the forcing acoustic field. As they respond to low-frequency, they are in general excited by low-frequency bulk waves 26,27 . In this section, we present the interest of using a bubble trapped in the axis of the Bessel evanescent field. Indeed, the well-known streaming capability of excited microbubble here competes with the strong inward radiation force associated with the Bessel field on which the bubble is trapped.
Gas bubbles of initial radius around r b > 25 μm are created by water electrolysis using a pair of electrodes, one of them being placed just on top of the plate center, when sound is present. Alignment with a mark on the bottom plate is ensured by means of a microscope. As a result of the acoustic field, the bubbles are attracted to the bottom emitting plate, where they remain anchored even after having switched the sound off. The resulting "pendent" bubble holds to the bottom glass by capillarity 26 with a contact angle of about 20°.
When sound is present, bubbles grow with time by rectified diffusion 28 allowing us to slowly vary the bubble radius up to 110 μm, keeping the forcing frequency f = 45 kHz constant. The surrounding liquid is seeded with microparticles of radius r p from 1 μm to 40 μm. A high speed imaging system is mounted on the microscope in order to image the fast bubble dynamics (see Methods).
At a low acoustic amplitudes, the bubble oscillates radially (breathing mode) for a large range of radius (typically μm). A maximum response is obtained around r b = 50 μm. When the acoustic amplitude is further increased, we observe the trigger of a parametric instability (Supplementary Movie 4 and Supplementary Figs. 8 and 9) as already reported for both tethered, free bubbles and confined flat bubbles [29][30][31] . In this regime, the streaming is expected to be stronger 32 and subharmonic surface waves propagate along the bubble interface, superimposed on the breathing mode. Overall, in the presence of particles, various patterns are observed going from more or less complex streaming loops (see Fig. 4a, left side) to bubble repulsion (Fig. 4b, c) or attraction (Fig. 4d) depending on the particle size, bubble diameter, confinement and applied voltage (see Supplementary Movies 5-9 for several examples).

Discussion
Classically, a free bubble resonant frequency can be estimated by ρ l q 28 (γ: adiabatic index, p 0 : static pressure). The confinement lowers the resonant frequency and broadens the bubble response (decrease of the quality factor). The present contact angle of 20°predicts a modified eigenfrequency f b0c = 0.83f b0 33 , or equivalently a resonant radius of 60 μm, in reasonable agreement with our measurements. The microstreaming from an axisymmetrically pulsating pendent bubble has been calculated by Elder 34 and is qualitatively sketched in Fig. 4a. Let us now try to give an interpretation of the observed behaviors by following this figure. In the absence of bubble, particles migrate radially inward (toward the Bessel beam axis), pushed by the above-studied near-field radiation force F rad . When a bubble is added, the induced outer streaming near the plate is directed outwards (see Fig. 4a, right side) so that both effects compete. Therefore, beads are likely to gather at a certain distance r eq away from the bubble center where both force F s and F rad balance. Indeed, as shown in Fig. 4b an additional ring at r = r eq away from the bubble is formed on top of the original and larger Bessel ring stemming from the plate mode (see also Supplementary Movie 6). Depending on their buoyancy (force F g in Fig. 4a), particles can either turn in the loops of the outer streaming (see Fig. 4a and Supplementary Movie 7 for 1 μm particles) or migrate to finally settle at r = r eq so that a clear depleted region appears between r = r b and r eq (see Fig. 4c for an example with HeLa cells). Let us estimate r eq : at the plate level, the bubble-induced outer streaming v s can be estimated by v s ¼ where α depends on the particle radius. Figure 4e (blue curve) shows the radial velocity resulting from both contributions (see also Supplementary Fig. 10 and Supplementary Movie 11). As expected, the contribution of the radiation force is small in comparison with the streaming force but both balance at r eq = 537 μm (horizontal velocity cancellation) close to the observed ring in Fig. 4e. Now, when the plate inward radiation force F rad dominates the outer streaming force F s particles are attracted towards the beam axis matching the bubble location. When approaching the bubble wall, particles will eventually be captured by the shortrange secondary radiation force F rad,b emanating from the pulsating bubble, as recently reported 27 . The attraction effect is maximized when the device is confined (so that the near-field radiation force is enhanced) and when the streaming is weak (for a non resonating bubble) -see Supplementary Movie 10 and Fig. 4d. In addition, as the capture mechanism depends on the combination of two radiation forces F rad and F rad,b (which both scale like r 3 p ) this regime is observed only for large enough particles (>40 μm) for which the streaming contribution is vanishingly small (F s~rp ).
Finally, for the case of tiny particles (r p < 5 μm), and provided that the bubble pulsation is strong enough, the near-field radiation force is in general too weak to compete with the streaming so that more classic continuous streaming loops are observed (both inner and outer) around the bubble (left side of Fig. 4a).
To summarize, the stable trapping of a microbubble in the Bessel beam axis enabled us to reverse the central plate pattern v s0 is the measured velocity at r 0 (v s (r 0 ) = 19 μm s −1 ). Blue curve: bead velocity obtained from the cumulative effects of the bubble microstreaming force (red curve) and the near-field plate radiation force. An equilibrium is obtained for r = r eq . Insert: overlay of minimal intensities over 10 s in the present experiment. Beads move outwards between the magenta and red circles (162 < r < 510 μm), and join an inner vortex ring for lower radii positions. The bubble pulsation amplitude is 4 μm and use bubbles as acoustic magnet for attracting, repelling or mixing the surrounding particles. We have demonstrated the possibility of creating an evanescent acoustic Bessel beam of order zero by low-frequency ultrasound. Interestingly, the subsonic regime of plate wave propagation results in the generation of unusually strong spatial gradients. Consequently, we have succeeded in arranging either microbeads, HeLa cells and bacteria in concentric ring patterns that correspond to the antinodes of the pressure Bessel field. As we have shown, particles are pushed by the strong near-field radiation force, whose expression differs from the conventional bulk one due to the evanescence of the field. When the beam is confined to a sub-wavelength cavity, the Bessel beam radial wavelength is decreased, enhancing the force and leading to some height dependent resonances. This field enhancement is very close to the one evidenced for slotted phononic crystal plates, arranged in a subwavelength cavity mode 18,20 with periodically grooved structures.
As recently shown in plasmonics, the confinement of optical vortices 35 or of evanescent vortex Bessel beam 36 is a promising approach to achieve powerful optical spanners. Likewise, we believe that adding an azimuthal phase control of the excitation will generate higher order evanescent acoustic Bessel beam and acoustic vortices. This strategy, recently demonstrated for acoustorotation in the case of evanescent plane waves 7 , opens the route toward flexible trapping and spinning of individual living cells in culture conditions. Overall, we believe that extending acoustic manipulation to the near-field domain will open unprecedented opportunities to fill the gap between conventional (propagative) acoustofluidics and the recent rise of phononics and acoustic metamaterials.

Methods
Device fabrication. The piezoelectric has a 4-mm-thick ring shape, with a 17-33mm internal and external diameters (NCE80, Noliac). The circular glass coverslip has a 20 mm diameter (Menzel-Gläser). The fixing double sided tape is cut to a ring shape of internal radius 9 mm with a cutting machine Craft Robo (Graphtec). Two contacts are made by fixing electric wires with silver conductive paint, and the resonance is measured with a spectrum analyzer (4195A, Hewlett Packard). For the unconfined study, the plastic cylinder is a section of a 50 mL Falcon.
Pressure measurements. The pressure measurements are performed using an hydrophone from Precision Acoustics, with a needle of 1.5 mm outer diameter, holding a 1 mm diameter polyvinylidene fluoride (PVDF) membrane.
Imaging. The device is mounted on the microscope with a home made aluminum and PMMA support (see Supplementary Fig. 3). The sub-periodic bubble dynamics are resolved with a high speed camera (Fastcam SA1.1, Photron) mounted on an inverted microscope (Eclipse, Nikon). Supplementary Movie 12 is obtained with a ×6 (×4 × 1.5) magnification and Hg illumination. The bacteria patterns are imaged with a large field camera (ORCA-flash4.0, Hamamatsu) mounted on a reflectedlight microscope (Zeiss Axioplan II) equipped for fluorescent imaging and a 5× objective.
Microparticles. All polystyrene microparticles are purchased from Fluka, with the indicated sizes referring to the particle diameter.
Blood samples. Whole human blood samples were obtained from healthy donors (Établissement Français du Sang (EFS), Grenoble, France) and were collected in citrate vacutainer tubes (Becton Dickinson, Le Pont de Claix, France). Samples were used without any dilution and the blood tubes were delivered three days after withdrawal and were kept at 4°C in a fridge for storage. The experiments were performed within three days after delivery.
Ethics statement. Experiments with blood are performed according to the ethical and legal standards of our blood supplier (EFS). Informed consent was given by blood donors.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request. Received: 7 January 2019 Accepted: 11 July 2019